Kris Humphries’ lawyer has been speaking with the lawyer for girlfriend Myla Sinanaj … trying to negotiate a non-disclosure agreement … for a price.

Sources connected with Kris tell us … his lawyer reached out to hers earlier today, trying to muzzle her from talking about their relationship. Our sources say Kris is nervous about the texts, emails and other documents she has relating to their relationship — things Kris wants to keep under wraps.

As for why Kris wants to muzzle Myla — his lawyers are demanding millions from Kim Kardashian, alleging she defrauded him and broke his heart. It’s hard to make the case when Kris is banging another chick two months after Kim files divorce docs.

We’re told, in addition to a non-disclosure agreement, Kris wants Myla to sign some sort of joint statement … again, for a price.